The Annals of Probability

A Finite Form of De Finetti's Theorem for Stationary Markov Exchangeability

Arif Zaman

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Abstract

De Finetti's theorem for stationary Markov exchangeability states that a sequence having a stationary and Markov exchangeable distribution is a mixture of Markov chains. A finite version of this theorem is given by considering a finite sequence $X_1,\ldots, X_n$ which is stationary and Markov exchangeable. It is shown that any portion of $k$ consecutive elements, say $X_1,\cdots, X_k$ for $k < n$, is nearly a mixture of Markov chains (the distance measured in the variation norm).

Article information

Source
Ann. Probab., Volume 14, Number 4 (1986), 1418-1427.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176992383

Digital Object Identifier
doi:10.1214/aop/1176992383

Mathematical Reviews number (MathSciNet)
MR866363

Zentralblatt MATH identifier
0608.60032

JSTOR
links.jstor.org

Subjects
Primary: 60J05: Discrete-time Markov processes on general state spaces
Secondary: 60G10: Stationary processes

Keywords
de Finetti's theorem Markov exchangeability stationary processes Markov chains

Citation

Zaman, Arif. A Finite Form of De Finetti's Theorem for Stationary Markov Exchangeability. Ann. Probab. 14 (1986), no. 4, 1418--1427. doi:10.1214/aop/1176992383. https://projecteuclid.org/euclid.aop/1176992383


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